Laser devices that operate with focused laser radiation in order to machine inorganic or organic material (e.g., human eye tissue) frequently exhibit controllable components that enable a scan function. With the scan function the radiation focus can be set precisely to differing positions in a plane orthogonal to the direction of propagation of the radiation (transverse scanning) or/and to differing positions along the direction of propagation of the radiation (longitudinal scanning). Examples of components that can serve for the scanning of laser radiation are swivel-mounted mirrors, deformable mirrors, electro-optical crystals, displaceably arranged lenses, lenses of variable refractive power, etc. Whenever scan components are mentioned within the scope of this disclosure, not only the optical components acting on the laser radiation are meant thereby, but rather also the totality of the components that are needed for scanning the laser radiation and that are capable of being influenced by electrical control signals of an electronic control arrangement. Accordingly, the scan components in the sense of the invention also include, in particular, the actuators that, where appropriate, are necessary for actuating the optical scan components and that are capable of being driven by the control signals of the control arrangement. Such actuators may, for example, include galvanometer drives, piezoelectric drives, motorized drives, controllable voltage-sources or current-sources, etc. It will be understood that the above enumeration of possible optical scan components and actuators is purely exemplary and is not to be understood as being restrictive.